Fall 2019 - University of Toronto
Prepared by: Behrad Vatankhahghadim
Contact: Behrad [dot] Vatankhahghadim [at] mail.UToronto.ca
Prologue
These course notes are developed for the students of Spacecraft Dynamics and Control (AER506) based on the following resources:
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AER506 Course Notes, C. J. Damaren, University of Toronto, Fall 2015
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AER506 Notes, based on lectures by G. M. T. D’Eleuterio, University of Toronto, Fall 2013
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Spacecraft Dynamics and Control: an Introduction, A. H. J. de Ruiter, C. J. Damaren, J. R. Forbes; Wiley, 2013
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Spacecraft Attitude Dynamics, P. C. Hughes; Dover, 2004
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Space Vehicle Dynamics and Control, B. Wie; American Institute of Aeronautics and Astronautics, 1998
These notes are meant as a supplement and not a substitute for the lectures. They do not include examples or tutorial problems discussed in class, nor do they elaborate on the concepts as much as the lectures are intended to do. They also make occasional references to the course’s required and recommended textbooks (the third and fourth items in the list above, respectively), and hence are not self-contained. It is hoped, nevertheless, that the students will find them useful for preparing for each lecture beforehand, for facilitating their in-class note-taking, and for reviewing the key concepts as the course progresses.
1 - Fundamentals
Vectrix Notation, Reference Frames, Rotation Matrices and Change of Frames, Attitude Representations
2 - Kinematics
Geometry of Motion, Definition and Properties of Angular Velocity, Vector Derivatives in Rotating Frames, Relating Angular Velocity to Attitude
3 - Dynamics
Science of Motion; Force/Momentum and Torque/Angular Momentum for Point Masses, Systems of Masses, and Rigid Bodies; Moment of Inertia Matrix and Its Properties
4 - Orbital Mechanics
Two-Body Problem, Constants of Orbital Motion, Kepler’s Laws and Newton’s Law of Gravitation, Polar Equation and Conic Sections, Anomalies
5 - Orbit Description and Determination
Position and Velocity from Classical Orbital Elements and Time, Orbital Elements from Position and Velocity, Lambert’s Problem of Orbit Determination, Porkchop Plots
6 - Orbital Perturbations
Effects of Perturbations on Orbital Parameters, Numerical Approaches, Gauss’ Variational Equations Parameters’ Rate of Change, J2 Perturbations
7 - Launch Vehicle Dynamics
Simplified Study of Forces on and Motion of Launch Vehicles, Focusing on Vertical Ascent, Turn-Over, and Gravity Turn Trajectories
8 - Orbital Manoeuvres
General Manoeuvres; Radial Thrust; Tangential Thrust, Hohmann Transfer, and Rendezvous; Normal Thrust
9 - Interplanetary Travel
Sphere of Influence, Hyperbolic Departure and Arrival Hyperbolae, Interplanetary Hohmann Transfer, Planetary Fly-By
10 - Restricted Three-Body Problem
Equations of Circular Restricted Three-Body Motion, Lagrange Points and Their Stability, Jacobi Integral and Hill Curves
11 - Stability
Linear Stability and Linear Mechanical Systems, Input/Output Stability, Lyapunov Stability, Lyapunov’s First Method
12 - Torque-Free Motion
Constants of Torque-Free Motion, Angular Velocity and Attitude History of an Inertially Axisymmetrical Body, Geometrical Interpretation of Torque-Free Rotation
13 - Spin Stabilization
Linear Stability of Simple Spins, Energy and Momentum Ellipsoids, Internal Energy Dissipation and Major Axis Rule
14 - Dual-Spin Stabilization
Dual-Spin Equations and Constants of Motion, Stability Conditions for Gyrostats with Nominally Non-Spinning Platforms and Principally-Aligned Wheels
15 - Energy Dissipation in Dual-Spins
Constrained Minimization Approach to Energy Dissipation, Stability Conditions in Presence of Dissipation for Gyrostats with Nominally Non-Spinning Platforms and Principally-Aligned Wheels
16 - Disturbance Torques
External Torques Affecting Attitude Motion: Magnetic, Aerodynamic, Solar Radiation Pressure and Gravity Gradient Torques
17 - Gravity Gradient Stabilization
Equations of Rotational Motion under Influence of Gravity Gradient, Pitch and Roll/Yaw Stability Conditions, Effects of Damping on Attitude Stability
18 - Active Attitude Control
Basics of Control Theory: Laplace Transform, Transfer Functions, System Interconnecions; Simple Feedback Attitude Controllers, Transient and Steady-State Performance in Reponse to Step Input
19 - Bias-Momentum Stabilization
Equations of Motion for Actively-Controlled Dual-Spin Spacecraft subject to Gravity Gradient Torques, Active Pitch Control and Roll/Yaw Control, Steady-State Performance
20 - Nonlinear Attitude Control (Not Covered - From 2018)
A Brief Introduction to Nonlinear Attitude Control, Nonlinear Equations of Rotational Motion, Stability of Rate Feedback